Advertisements
Advertisements
प्रश्न
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
x3 + y3 = 4ax
Advertisements
उत्तर
x3 + y3 = 4ax .....(1)
Differentiating both sides w.r.t. x, we get
`3"x"^2 + 3"y"^2 "dy"/"dx" = 4"a" xx 1`
∴ `3"x"^2 + 3"y"^2 "dy"/"dx" = 4"a"`
Substituting the value of 4a in (1), we get
`"x"^3 + "y"^3 = (3"x"^2 + 3"y"^2 "dy"/"dx")"x"`
∴ `"x"^3 + "y"^3 = 3"x"^3 + 3"xy"^2 "dy"/"dx"`
∴ `2"x"^3 + 3"xy"^2 "dy"/"dx" - "y"^3 = 0`
This is the required D.E.
APPEARS IN
संबंधित प्रश्न
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y2 = (x + c)3
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = a + `"a"/"x"`
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = e−2x (A cos x + B sin x)
Find the differential equation of all circles having radius 9 and centre at point (h, k).
Form the differential equation of family of lines parallel to the line 2x + 3y + 4 = 0.
Form the differential equation of all parabolas whose axis is the X-axis.
Solve the following differential equation:
`log ("dy"/"dx") = 2"x" + 3"y"`
Solve the following differential equation:
`"y" - "x" "dy"/"dx" = 0`
Solve the following differential equation:
`"sec"^2 "x" * "tan y" "dx" + "sec"^2 "y" * "tan x" "dy" = 0`
Solve the following differential equation:
`(cos^2y)/x dy + (cos^2x)/y dx` = 0
Solve the following differential equation:
`"y"^3 - "dy"/"dx" = "x"^2 "dy"/"dx"`
Reduce the following differential equation to the variable separable form and hence solve:
`"x + y""dy"/"dx" = sec("x"^2 + "y"^2)`
Choose the correct option from the given alternatives:
The differential equation of y = `"c"^2 + "c"/"x"` is
Choose the correct option from the given alternatives:
The solution of `("x + y")^2 "dy"/"dx" = 1` is
The particular solution of `dy/dx = xe^(y - x)`, when x = y = 0 is ______.
In the following example verify that the given function is a solution of the differential equation.
`"x"^2 = "2y"^2 log "y", "x"^2 + "y"^2 = "xy" "dx"/"dy"`
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
(y - a)2 = b(x + 4)
Solve the following differential equation:
`"dy"/"dx" + "y cot x" = "x"^2 "cot x" + "2x"`
Solve the following differential equation:
`"dx"/"dy" + "8x" = 5"e"^(- 3"y")`
Find the particular solution of the following differential equation:
`"dy"/"dx" - 3"y" cot "x" = sin "2x"`, when `"y"(pi/2) = 2`
Find the particular solution of the following differential equation:
y(1 + log x) = (log xx) `"dy"/"dx"`, when y(e) = e2
Find the particular solution of the following differential equation:
`2e ^(x/y) dx + (y - 2xe^(x/y)) dy = 0," When" y (0) = 1`
Find the differential equation of family of lines making equal intercepts on coordinate axes
Find the general solution of `("d"y)/("d"x) = (1 + y^2)/(1 + x^2)`
Find the differential equation by eliminating arbitrary constants from the relation x2 + y2 = 2ax
Find the differential equation by eliminating arbitrary constants from the relation y = (c1 + c2x)ex
Find the differential equation from the relation x2 + 4y2 = 4b2
The differential equation having y = (cos-1 x)2 + P (sin-1 x) + Q as its general solution, where P and Q are arbitrary constants, is
Find the differential equation of the family of all non-vertical lines in a plane
Find the differential equation of the family of all non-horizontal lines in a plane
Find the differential equation of the family of circles passing through the origin and having their centres on the x-axis
Find the differential equation of the curve represented by xy = aex + be–x + x2
The rate of disintegration of a radio active element at time t is proportional to its mass, at the time. Then the time during which the original mass of 1.5 gm. Will disintegrate into its mass of 0.5 gm. is proportional to ______.
If `x^2 y^2 = sin^-1 sqrt(x^2 + y^2) + cos^-1 sqrt(x^2 + y^2)`, then `"dy"/"dx"` = ?
The elimination of the arbitrary constant m from the equation y = emx gives the differential equation ______.
The differential equation representing the family of parabolas having vertex at origin and axis along positive direction of X-axis is ______.
Solve the following differential equation:
`xsin(y/x)dy = [ysin(y/x) - x]dx`
If y = (tan–1 x)2 then `(x^2 + 1)^2 (d^2y)/(dx^2) + 2x(x^2 + 1) (dy)/(dx)` = ______.
Solve the differential equation
cos2(x – 2y) = `1 - 2dy/dx`
If 2x = `y^(1/m) + y^(-1/m)`, then show that `(x^2 - 1) (dy/dx)^2` = m2y2
Solve the differential equation
ex tan y dx + (1 + ex) sec2 y dy = 0
